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    "<h1>Lecture 8: 推断统计——假设检验</h1><h2>Instructor: Dr. Hu Chuan-Peng</h2><p></p>"
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    "<h2>回顾</h2><p>上节课介绍了后验本质上已经是推断统计中的“参数估计”，并且也介绍了如何报告后验(credible intervals, CrI).</p><p>本讲我们继续介绍推断统计中的假设检验。</p><p></p><p>在贝叶斯推断中，最关键的是理解假设检验与后验之间的关系，从而理解当前贝叶斯统计中存在了多种指标及其内在的联系。</p><p></p><img src=\"https://cdn.kesci.com/upload/sm7veon5ei.png?imageView2/0/w/720/h/960\" alt=\"Image Name\"><p></p>"
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    "<p>本节课将从心理学的视角，介绍假设检验及其贝叶斯方法：</p><h2><strong>Outline</strong></h2><ol><li><p>贝叶斯框架下的假设检验</p></li><li><p>基于后验分布的统计推断</p></li><li><p>基于贝叶斯因子的统计推断</p></li></ol><p>对于每种统计推断方法，我们将从以下三种应用作为展开：</p><ul><li><p>Testing against the point-null</p></li></ul><ul><li><p>Testing against a null-region</p></li><li><p>Directional hypotheses</p></li></ul><p></p>"
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    "<h2>1.贝叶斯框架下的假设检验</h2><h3>1.1 传统的假设检验方法(NHST)</h3><p>🧑‍💻在学习贝叶斯框架下的假设检验方法前，我们先简单回顾一下传统统计中的零假设显著性检验（Null Hypothesis Significance Test, NHST）。</p><p>频率学派的假设检验主要是基于概率性质的反证法所实现的推论统计方法。即承认如下前提:小概率事件(发生概率小于0.05的事件)在单次抽样中不会发生。</p><p>在传统的假设检验框架中，研究者需要根据研究对总体做互斥的两种假设，即零假设$ H_0 $和备择假设$ H_1 $：</p><blockquote><p><strong>零假设（Null Hypothesis，$ H_0 $）</strong>：表示没有效应或差异的假设。在许多情况下，零假设代表“无差异”或“无效应”，例如认为两组数据的均值没有显著差异。</p></blockquote><blockquote><p><strong>备择假设（Alternative Hypothesis，$ H_1 $）</strong>：表示零假设不成立时的假设，通常认为有显著效应或差异。</p></blockquote><p></p><p></p>"
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    "<p>传统假设检验的核心概念还包括：</p><p></p><ul><li><p><strong>Alpha（$ \\alpha $）</strong>：显著性水平，通常设定为 0.05，表示在零假设（$ H_0 $）成立的情况下，错误拒绝零假设（$ H_0 $）的概率。换句话说，alpha（$ \\alpha $）是我们愿意接受的第一类错误概率（假阳性）。</p></li><li><p><strong>$ P $值</strong>：是指在零假设成立的前提下，观察到当前或更极端数据的概率。如果 $ P $ 值小于等于 $ \\alpha $，传统统计学的框架下通常会拒绝零假设，认为数据提供了足够的证据支持备择假设。</p></li><li><p>$统计检验力(statistical power)$: 当零假设不成立（即备择假设成立时），当前模型有多大可能拒绝零假设。</p></li></ul><p></p><ul><li><p>传统的假设检验方法主要依赖于 $ P $ 值，这一方法在统计学中应用广泛，但也存在多个问题：</p><ol><li><p><strong>假阳性结果</strong>：研究者可能会通过操纵p值来达到显著性，如增加样本量或调整变量，这会导致假阳性结果，误导后续研究。&nbsp; &nbsp;</p></li><li><p><strong>忽视效应大小</strong>：$ P $ 值无法提供效应大小的信息，仅仅是显著与否的二分判断，不能全面反映数据的实际意义。&nbsp; &nbsp; &nbsp; &nbsp;</p></li><li><p><strong>不考虑先验信息</strong>：传统假设检验忽略了先验知识和理论背景，仅关注数据本身，无法有效利用已有的研究成果。</p></li><li><p><strong>无法为直接为零假设提供支持</strong>：不显著结果不代表零假设为真。</p></li></ol></li></ul><p></p><img src=\"https://cdn.kesci.com/upload/smw36cj13b.png?imageView2/0/w/480/h/960\" alt=\"Image Name\"><blockquote><p>胡传鹏等(2018). 贝叶斯因子及其在JASP中的实现. <em>心理科学进展</em> <br>吴凡, 顾全, 施壮华, 高在峰, 沈模卫. (2018). 跳出传统假设检验方法的陷阱——贝叶斯因子在心理学研究领域的应用. <em>应用心理学</em></p></blockquote><p></p>"
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    "<h3>1.2 假设检验的统一框架 (Smiley et al., 2023; Kiers &amp; Tendeiro, 2025)</h3><p></p><table style=\"min-width: 75px;\"><colgroup><col style=\"min-width: 25px;\"><col style=\"min-width: 25px;\"><col style=\"min-width: 25px;\"></colgroup><tbody><tr><th colspan=\"1\" rowspan=\"1\"><p>检验类型</p></th><th colspan=\"1\" rowspan=\"1\"><p>零区间</p></th><th colspan=\"1\" rowspan=\"1\"><p>感兴趣区间</p></th></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>双侧NHST</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ = 0</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &gt; 0 or δ &lt; 0</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>单侧NHST</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &lt; 0</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &gt; 0</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>双侧最小效应检验</p></td><td colspan=\"1\" rowspan=\"1\"><p>−c &lt; δ &lt; c</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &lt; −c or δ &gt; c</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>单侧最小效应检验</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &lt; c</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &gt; c</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>等价性检验</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &lt; −c or δ &gt; c</p></td><td colspan=\"1\" rowspan=\"1\"><p>−c &lt; δ &lt; c</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>非劣性检验</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &lt; −c</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &gt; −c</p></td></tr></tbody></table><blockquote><p>Kiers, H. A. L., &amp; Tendeiro, J. N. (2025). Bridging Null Hypothesis Testing and Estimation: A Practical Guide to Statistical Conclusion Drawing From Research in Psychology. <em>Advances in Methods and Practices in Psychological Science</em>, <em>8</em>(3), 25152459251365960. <a target=\"_blank\" rel=\"noopener noreferrer nofollow\" href=\"https://doi.org/10.1177/25152459251365960\">https://doi.org/10.1177/25152459251365960</a></p><p>Smiley, A. H., Glazier, J. J., &amp; Shoda, Y. (2023). Null regions: A unified conceptual framework for statistical inference. <em>Royal Society Open Science</em>, <em>10</em>(11), 221328. <a target=\"_blank\" rel=\"noopener noreferrer nofollow\" href=\"https://doi.org/10.1098/rsos.221328\">https://doi.org/10.1098/rsos.221328</a></p></blockquote><p></p>"
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    "<h3>1.3 贝叶斯框架下的假设检验优势</h3><p>与传统假设检验方法相比，贝叶斯框架下的方法具有以下几方面的优势：</p><ol><li><p><strong>可以对假设一视同仁：</strong> 同时评估$ H_0 $和$ H_1 $的可能性，能够为$ H_0 $提供支持证据，解决传统假设检验难以证明$ H_0 $成立的问题。&nbsp;</p></li><li><p><strong>结合先验信息：</strong> 贝叶斯因子分析可以利用先验知识，将前人的研究成果与当前数据结合，提供更为全面的证据评估。&nbsp; &nbsp; &nbsp; &nbsp;</p></li><li><p><strong>避免<em>p</em>值操纵：</strong> 贝叶斯因子的计算基于全数据集，不受单个数据点的影响，能够有效避免p值操纵带来的假阳性结果。&nbsp; &nbsp; &nbsp;</p></li><li><p><strong>支持多模型比较：</strong> 贝叶斯因子不仅适用于二元假设检验，还可以用于比较多个模型的适用性，提供更为灵活的统计分析工具。</p></li><li><p><strong>可以直接支持零假设</strong>。</p></li></ol><p></p><blockquote><p>吴凡, 顾全, 施壮华, 高在峰, 沈模卫. (2018). 跳出传统假设检验方法的陷阱——贝叶斯因子在心理学研究领域的应用. <em>应用心理学</em></p><p>许岳培, 陆春雷, 王珺, 宋琼雅, 贾彬彬, 胡传鹏. (2022). 评估零效应的三种统计方法. 应用心理学, <em>28</em>(4), 369–384.</p></blockquote><p></p>"
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    "<p><strong>以Beta-Binomial模型在Stan中的实现为例</strong></p><p>仍然以随机点运动任务为例，每个试验中参与者判断正确的概率用 $ \\pi $ 表示。</p><p></p><p><strong>模型假设</strong></p><ul><li><p>判断正确概率 $ \\pi $ 服从 <strong>Beta 分布</strong>分布：</p></li></ul><p>$$ \\begin{equation} \\pi \\sim \\text{Beta}(\\alpha, \\beta) \\end{equation} $$</p><ul><li><p>在每次试验中，参与者的成功次数 $ Y $ 服从 <strong>Binomial 分布</strong>：</p></li></ul><p>$$ \\begin{equation} Y \\sim \\text{Binomial}(n, \\pi) \\end{equation} $$</p><p>其中，$ n $是试验的总次数，$ Y $是成功次数。</p><p></p><p><strong>模型设定</strong></p><p>在这个例子中，我们可以使用Beta-Binomial 模型来表示：</p><p></p><blockquote><p>数据: 总试验数为n=10，成功次数为9 $ (Y = 9) $<br>先验分布为：$ \\pi \\sim \\text{Beta}(2, 2) $<br>似然函数为：$ Y|\\pi \\sim \\text{Bin}(n, \\pi) $</p></blockquote><p></p>"
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      "Chain 4: Iteration: 2000 / 5000 [ 40%]  (Sampling)\n",
      "Chain 4: Iteration: 2500 / 5000 [ 50%]  (Sampling)\n",
      "Chain 4: Iteration: 3000 / 5000 [ 60%]  (Sampling)\n",
      "Chain 4: Iteration: 3500 / 5000 [ 70%]  (Sampling)\n",
      "Chain 4: Iteration: 4000 / 5000 [ 80%]  (Sampling)\n",
      "Chain 4: Iteration: 4500 / 5000 [ 90%]  (Sampling)\n",
      "Chain 4: Iteration: 5000 / 5000 [100%]  (Sampling)\n",
      "Chain 4: \n",
      "Chain 4:  Elapsed Time: 0.004 seconds (Warm-up)\n",
      "Chain 4:                0.016 seconds (Sampling)\n",
      "Chain 4:                0.02 seconds (Total)\n",
      "Chain 4: \n"
     ]
    }
   ],
   "source": [
    "# 准备数据\n",
    "stan_data <- list(N = 118,Y = 99)\n",
    "\n",
    "# 定义模型\n",
    "stan_model_code <- \"\n",
    "data {\n",
    "  int<lower=0> N;       \n",
    "  int<lower=0, upper=N> Y; \n",
    "}\n",
    "parameters {\n",
    "  real<lower=0, upper=1> pi;\n",
    "}\n",
    "model {\n",
    "  pi ~ beta(2, 2);\n",
    "  Y ~ binomial(N, pi);\n",
    "}\n",
    "\"\n",
    "\n",
    "# 进行采样\n",
    "fit_bb <- stan(\n",
    "  model_code = stan_model_code,      # 定义的模型或模型文件路径\n",
    "  data = stan_data,                  # 输入数据\n",
    "  chains = 4,                        # 马尔可夫链数量\n",
    "  iter = 5000,                       # 总迭代次数（每个链）\n",
    "  warmup = 1000,                     # 热身迭代次数（不保存）\n",
    "  seed = 84735\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "hide_input": false,
    "id": "3BFEF390136547D5AACF31FB957B6C27",
    "jupyter": {},
    "notebookId": "690a86a8ae50d8e7fdf63a45",
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": [],
    "trusted": true,
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
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b3ts5q+bDK6JlKXkd19GqOVgvi/6hbd16IUCT8BiXIChMb+tpayoGY2dZZIMgV+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EMF8Ia95Ef145ISdwrCwl3zjtbJDbCH/qTVPEFV+cLX\ni0egKzo7qvloJu8lbit+AatnXKvaqRr8lgK709FDl9nzDo2atUADm4fn2TUKu0Q37gP+rVdz\ny7/UcN/OPf59OSf6BZblbh4KZW5kc3RyZWFtCmVuZG9iagoxOCAwIG9iagogICAyNzUKZW5k\nb2JqCjE5IDAgb2JqCjw8IC9UeXBlIC9YUmVmCiAgIC9MZW5ndGggNzkKICAgL0ZpbHRlciAv\nRmxhdGVEZWNvZGUKICAgL1NpemUgMjAKICAgL1cgWzEgMiAyXQogICAvUm9vdCAxNyAwIFIK\nICAgL0luZm8gMTYgMCBSCj4+CnN0cmVhbQp4nGNgYPj/n4mBi4EBRDAxmtxmYGBk4AcSJodB\nYhxAVhCIa+oBIk4BiZBSEOs+kPBXAxF2QCLgMYj4BTGFEUQwM4b+BYqFiTAwAACi7Q1XCmVu\nZHN0cmVhbQplbmRvYmoKc3RhcnR4cmVmCjIyMDM2CiUlRU9GCg==",
      "text/html": [
       "<img src=\"https://cdn.kesci.com/upload/rt/3BFEF390136547D5AACF31FB957B6C27/t5ckp5lsao.svg\">"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "application/pdf": {
       "height": 420,
       "width": 420
      },
      "image/jpeg": {
       "height": 420,
       "width": 420
      },
      "image/png": {
       "height": 420,
       "width": 420
      },
      "image/svg+xml": {
       "height": 420,
       "isolated": true,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp <- bayesplot::mcmc_areas(fit_bb, regex_pars = \"pi\",  prob = 0.8) +\n",
    " labs(\n",
    "   title = \"Posterior distributions\",\n",
    "   subtitle = \"with medians and 80% intervals\"\n",
    " ) +\n",
    " papaja::theme_apa()\n",
    "\n",
    " pp"
   ]
  },
  {
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    "<p></p><p>🤔假设我们在一篇报道中看到这样一种描述：在随机点运动任务中，成功次数占比为80%。</p><p></p><p>如何根据这个数据结果判断改成功率是否大于随机判断水平 50% 呢？ <br></p><p>我们同时考虑两种可能性：成功次数 $\\pi$ 的比例是否与 50% 相同，此时备择假设和虚无假设可以写成：</p><p></p><p>$ H_0: \\pi = 0.5 $</p><p></p><p>$H_a: \\pi \\ne 0.5$</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "<h2>2. 基于后验分布的统计推断</h2><h3>2.1 Testing against the point-null：通过 HDI 进行检验</h3><p></p><p>沿用之前的例子，已经知道先验分布为 $Beta(2, 2)$； 后验分布为 $Beta(101, 21)$。</p><p></p><p>为了检验 $\\pi$ 是否显著不同于 0.5，我们可以计算 <strong>后验分布的 HDI</strong>（Highest Density Interval），这是一种包含后验分布中最高概率密度的区间。通常 HDI 表示一个区间，比如 95% HDI，意味着该区间包含了后验分布中的 95% 的概率质量。</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "runtime": {
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   "source": [
    "<p><strong>计算 HDI</strong></p><p></p><p>HDI 是后验分布中包含最高密度的区间，我们通常计算 95% HDI，这意味着该区间包含后验分布中 95% 的概率质量。HDI 的定义要求该区间 $[\\pi_\\text{low}, \\pi_\\text{high}]$ 满足以下条件：</p><p><br></p><p>1. 对于任何 $\\pi$ 在区间 $[\\pi_\\text{low}, \\pi_\\text{high}]$ 外的点，它的密度都小于区间内的点的密度，即：</p><p><br></p><p>$f(\\pi_\\text{low} | \\alpha, \\beta) = f(\\pi_\\text{high} | \\alpha, \\beta)$</p><p><br></p><p>2. 该区间内的概率质量为 95%：</p><p></p><p>$\\int_{\\pi_\\text{low}}^{\\pi_\\text{high}} f(\\pi | \\alpha, \\beta) d\\pi = 0.95$</p>"
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  {
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    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A bayestestR_hdi: 1 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Parameter</th><th scope=col>CI</th><th scope=col>CI_low</th><th scope=col>CI_high</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.95</td><td>0.7588729</td><td>0.8909902</td><td>trace$pi</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A bayestestR\\_hdi: 1 × 4\n",
       "\\begin{tabular}{llll}\n",
       " Parameter & CI & CI\\_low & CI\\_high\\\\\n",
       " <dbl> & <dbl> & <dbl> & <chr>\\\\\n",
       "\\hline\n",
       "\t 0.95 & 0.7588729 & 0.8909902 & trace\\$pi\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A bayestestR_hdi: 1 × 4\n",
       "\n",
       "| Parameter &lt;dbl&gt; | CI &lt;dbl&gt; | CI_low &lt;dbl&gt; | CI_high &lt;chr&gt; |\n",
       "|---|---|---|---|\n",
       "| 0.95 | 0.7588729 | 0.8909902 | trace$pi |\n",
       "\n"
      ],
      "text/plain": [
       "  Parameter CI        CI_low    CI_high \n",
       "1 0.95      0.7588729 0.8909902 trace$pi"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# get posterior\n",
    "trace <- rstan::extract(fit_bb)\n",
    "trace_par <- as.data.frame(trace$pi)\n",
    "\n",
    "# get HDI\n",
    "bayestestR::hdi(trace_par,ci = 0.95) # 可自行更改不同范围的HDI区间。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "C21A800A9A754BEEBE2DC3D7F9FE0BA7",
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   "source": [
    "<p><strong>结果解释</strong></p><p></p><p>经过计算，得到的 95% HDI 区间为 $[0.75, 0.89]$。接下来，我们要验证这个区间是否包含 0.5：</p><p></p><p>- 该区间为 $[0.75, 0.89]$。</p><p>- 0.5 不在这个区间内。</p><p></p><p>因此，95% HDI 区间不包含 0.5，表明在 95% 的可信水平下，成功率 $\\pi$ 与 0.5 存在差异。基于这一结果，我们可以拒绝虚无假设 $H_0: \\pi = 0.5$，认为成功率 $\\pi$ 显著不同于 0.5。</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "952C02BFC358464190238D608D88A0B3",
    "jupyter": {},
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   "source": [
    "<h3>2.2 Testing against a null-region：通过 HDI + ROPE 进行检验</h3><p></p><p><strong>ROPE</strong>（Region of Practical Equivalence，实际等效区间）是一种贝叶斯统计中的概念，用来定义在实践中认为与虚无假设无显著差异的区域。通过结合 HDI 和 ROPE，我们可以进一步检验成功率 $\\pi$ 是否在实践中显著不同于 0.5。 <br></p><p>在这个例子中，我们假设 ROPE 的范围为 $[0.4, 0.6]$。这意味着如果成功率 $\\pi$ 落入这个区间，我们认为 $\\pi$ 在实践中与随机判断水平 0.5 没有显著差异。因此，我们的目标是判断 95% HDI 区间是否完全落在 ROPE 内，完全在 ROPE 外，或者部分重合。</p><p></p><blockquote><p>注意：ROPE需要我们根据具体情况进行调整。 一般情况下需要参考经验值或文献中的建议。</p></blockquote><p></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0D28A3A791B047E1A143F8B03AB560E6",
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    "notebookId": "690a86a8ae50d8e7fdf63a45",
    "runtime": {
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    "slideshow": {
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   "source": [
    "<p><strong>检验步骤</strong></p><p></p><p>我们已经知道 95% HDI 区间为 $[0.75, 0.89]$。接下来，我们需要将这个区间与 ROPE 区间 $[0.4, 0.6]$ 进行比较：</p><p><br></p><p>- HDI 区间为 $[0.75, 0.89]$。</p><p>- ROPE 区间为 $[0.4, 0.6]$。</p><p><br></p><p>接下来，我们考虑三种可能的情况：</p><p></p><p>- <strong>HDI 完全落在 ROPE 之内</strong>：如果 95% HDI 完全在 $[0.4, 0.6]$ 之内，那么可以认为 $\\pi$ 在实践中与 0.5 无差异。</p><p>- <strong>HDI 完全落在 ROPE 之外</strong>：如果 95% HDI 完全在 $[0.4, 0.6]$ 之外，那么可以认为 $\\pi$ 在实践中不同于 0.5。</p><p>- <strong>HDI 与 ROPE 部分重合</strong>：如果 95% HDI 区间与 ROPE 有部分重合，那么可以认为不确定 $\\pi$ 是否不同于 0.5。</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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    "id": "702EB0E1060F43F1A101CCA9B43993C5",
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    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A rope: 1 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Parameter</th><th scope=col>CI</th><th scope=col>ROPE_low</th><th scope=col>ROPE_high</th><th scope=col>ROPE_Percentage</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>trace$pi</td><td>0.95</td><td>0.4</td><td>0.6</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A rope: 1 × 5\n",
       "\\begin{tabular}{lllll}\n",
       " Parameter & CI & ROPE\\_low & ROPE\\_high & ROPE\\_Percentage\\\\\n",
       " <chr> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t trace\\$pi & 0.95 & 0.4 & 0.6 & 0\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A rope: 1 × 5\n",
       "\n",
       "| Parameter &lt;chr&gt; | CI &lt;dbl&gt; | ROPE_low &lt;dbl&gt; | ROPE_high &lt;dbl&gt; | ROPE_Percentage &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| trace$pi | 0.95 | 0.4 | 0.6 | 0 |\n",
       "\n"
      ],
      "text/plain": [
       "  Parameter CI   ROPE_low ROPE_high ROPE_Percentage\n",
       "1 trace$pi  0.95 0.4      0.6       0              "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# get ROPE\n",
    "bayestestR::rope(trace_par,range = c(0.4, 0.6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "DE41EC24970D4ACABBE79C66A985D861",
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   "source": [
    "<p><strong>结果分析</strong>  </p><p><br></p><p>在我们的例子中，HDI 区间 $[0.75, 0.89]$ 完全位于 ROPE 区间 $[0.4, 0.6]$ 之外。这意味着我们可以认为 $\\pi$ 在实践中与 0.5 存在差异，且成功率 $\\pi$ 高于 50%。  </p><p><br></p><p>HDI 区间 $[0.75, 0.89]$ 完全落在 ROPE 之外，这表明成功率 $\\pi$ 在实践中不同于随机判断水平 0.5。结合 HDI 和 ROPE 的结果，我们可以进一步确认成功率 $\\pi$ 高于 0.5。  </p><p><br></p><p>因此，基于 HDI + ROPE 的检验结果，我们可以认为成功率 $\\pi$ 不仅在统计学上（通过 HDI 检验），而且在实践中（通过 ROPE 检验）都不同于 50%。</p>"
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NEr5k0uNUPSS83ysGCRtto0p/pPN91X+tiUEENlVBaVlEfi8iol10T9WIkgmjRW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\nbmRzdHJlYW0KZW5kb2JqCnN0YXJ0eHJlZgoxNDU4NQolJUVPRgo=",
      "text/html": [
       "<img src=\"https://cdn.kesci.com/upload/rt/EB07866680B64C8CA8EE37CA1B5C32BC/t5ckq5ob0z.svg\">"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "application/pdf": {
       "height": 420,
       "width": 420
      },
      "image/jpeg": {
       "height": 420,
       "width": 420
      },
      "image/png": {
       "height": 420,
       "width": 420
      },
      "image/svg+xml": {
       "height": 420,
       "isolated": true,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "result <- bayestestR::rope(trace_par,range = c(0.4, 0.6))\n",
    "\n",
    "plot(result, rope_color = \"grey70\") + papaja::theme_apa()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BA6253BBD8DE4A8BAF81CB7BEBF89BAE",
    "jupyter": {},
    "notebookId": "690a86a8ae50d8e7fdf63a45",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "<p>思考：以上的HDI+ROPE属于以下哪一种检验？</p><ul><li><p>双侧最小效应检验</p></li><li><p>单侧最小效应检验</p></li><li><p>等价性检验</p></li><li><p>非劣性检验</p></li></ul><p></p>"
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    "<h3>2.3 Extend to Directional hypotheses：六种检验类型演示</h3><p>下面，我们将展示传统贝叶斯统计在六种假设检验框架下的实现。</p><p></p><p><strong>假设检验的统一框架 (Smiley et al., 2023; Kiers &amp; Tendeiro, 2025)</strong></p><p></p><table style=\"min-width: 75px;\"><colgroup><col style=\"min-width: 25px;\"><col style=\"min-width: 25px;\"><col style=\"min-width: 25px;\"></colgroup><tbody><tr><th colspan=\"1\" rowspan=\"1\"><p>检验类型</p></th><th colspan=\"1\" rowspan=\"1\"><p>零区间</p></th><th colspan=\"1\" rowspan=\"1\"><p>感兴趣区间</p></th></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>双侧NHST</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ = 0</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &gt; 0 or δ &lt; 0</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>单侧NHST</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &lt; 0</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &gt; 0</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>双侧最小效应检验</p></td><td colspan=\"1\" rowspan=\"1\"><p>−c &lt; δ &lt; c</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &lt; −c or δ &gt; c</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>单侧最小效应检验</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &lt; c</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &gt; c</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>等价性检验</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &lt; −c or δ &gt; c</p></td><td colspan=\"1\" rowspan=\"1\"><p>−c &lt; δ &lt; c</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>非劣性检验</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &lt; −c</p></td><td colspan=\"1\" rowspan=\"1\"><p>δ &gt; −c</p></td></tr></tbody></table><blockquote><p>Kiers, H. A. L., &amp; Tendeiro, J. N. (2025). Bridging Null Hypothesis Testing and Estimation: A Practical Guide to Statistical Conclusion Drawing From Research in Psychology. <em>Advances in Methods and Practices in Psychological Science</em>, <em>8</em>(3), 25152459251365960. <a target=\"_blank\" rel=\"noopener noreferrer nofollow\" href=\"https://doi.org/10.1177/25152459251365960\">https://doi.org/10.1177/25152459251365960</a></p><p>Smiley, A. H., Glazier, J. J., &amp; Shoda, Y. (2023). Null regions: A unified conceptual framework for statistical inference. <em>Royal Society Open Science</em>, <em>10</em>(11), 221328. <a target=\"_blank\" rel=\"noopener noreferrer nofollow\" href=\"https://doi.org/10.1098/rsos.221328\">https://doi.org/10.1098/rsos.221328</a></p></blockquote><p></p>"
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    {
     "name": "stdout",
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     "text": [
      "\n",
      "=== bayestestR ROPE Analysis (95% CI) ===\n",
      "\u001b[34m# Proportion of samples inside the ROPE [0.40, 0.60]:\n",
      "\n",
      "\u001b[39mInside ROPE\n",
      "-----------\n",
      "0.00 %     \n",
      "\n",
      "\n",
      "95% Highest Density Interval (HDI): 0.7589 to 0.891 \n",
      "Posterior Mean of π: 0.8273 \n",
      "Posterior Median of π: 0.8292 \n",
      "HDI fully within ROPE [0.4, 0.6]? NO \n"
     ]
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NHqIgkWzS5Sj0WriyRYtLpIjEWriyRYtLhIHRatLpJg0eoiCRatLpJg0a2nFItW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      "text/html": [
       "<img src=\"https://cdn.kesci.com/upload/rt/E6184A64E4C1483287CF7E98D9429945/t5ckqm92sp.svg\">"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
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       "height": 420,
       "width": 420
      },
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     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ============================================\n",
    "# 1. 提取后验样本（直接使用 pi）\n",
    "# ============================================\n",
    "posterior_samples <- extract(fit_bb)\n",
    "pi_posterior <- posterior_samples$`pi`  \n",
    "\n",
    "# ============================================\n",
    "# 2. 定义假设检验函数（基于 pi，ROPE = [0.4, 0.6]）\n",
    "# ============================================\n",
    "\n",
    "# ROPE Test: Practical equivalence to 0.5 with ROPE = [0.4, 0.6]\n",
    "rope_test <- function(samples, rope_lower = 0.4, rope_upper = 0.6) {\n",
    "  null_region <- samples <= rope_lower | samples >= rope_upper   # outside ROPE\n",
    "  interest_region <- samples > rope_lower & samples < rope_upper  # inside ROPE\n",
    "  \n",
    "  list(\n",
    "    name = \"ROPE Test (Practical Equivalence)\",\n",
    "    null = paste0(\"π ≤ \", rope_lower, \" or π ≥ \", rope_upper, \" (outside ROPE)\"),\n",
    "    interest = paste0(rope_lower, \" < π < \", rope_upper, \" (inside ROPE)\"),\n",
    "    p_null = sum(null_region) / length(samples),\n",
    "    p_interest = sum(interest_region) / length(samples),\n",
    "    rope_lower = rope_lower,\n",
    "    rope_upper = rope_upper\n",
    "  )\n",
    "}\n",
    "\n",
    "# 单侧 NHST: H0: π ≤ 0.5 vs H1: π > 0.5\n",
    "one_sided_nhst <- function(samples, null_val = 0.5) {\n",
    "  null_region <- samples <= null_val\n",
    "  interest_region <- samples > null_val\n",
    "  \n",
    "  list(\n",
    "    name = \"One-sided NHST\",\n",
    "    null = paste0(\"π ≤ \", null_val),\n",
    "    interest = paste0(\"π > \", null_val),\n",
    "    p_null = sum(null_region) / length(samples),\n",
    "    p_interest = sum(interest_region) / length(samples),\n",
    "    null_val = null_val\n",
    "  )\n",
    "}\n",
    "\n",
    "# 双侧最小效应检验: H0: π ∈ [0.4, 0.6] (no meaningful effect)\n",
    "two_sided_met <- function(samples, rope_lower = 0.4, rope_upper = 0.6) {\n",
    "  null_region <- samples > rope_lower & samples < rope_upper\n",
    "  interest_region <- samples <= rope_lower | samples >= rope_upper\n",
    "  \n",
    "  list(\n",
    "    name = \"Two-sided Minimal Effect Test\",\n",
    "    null = paste0(rope_lower, \" < π < \", rope_upper, \" (trivial effect)\"),\n",
    "    interest = paste0(\"π ≤ \", rope_lower, \" or π ≥ \", rope_upper, \" (meaningful effect)\"),\n",
    "    p_null = sum(null_region) / length(samples),\n",
    "    p_interest = sum(interest_region) / length(samples),\n",
    "    rope_lower = rope_lower,\n",
    "    rope_upper = rope_upper\n",
    "  )\n",
    "}\n",
    "\n",
    "# 单侧最小效应检验: H0: π ≤ 0.6 vs H1: π > 0.6\n",
    "one_sided_met <- function(samples, threshold = 0.6) {\n",
    "  null_region <- samples <= threshold\n",
    "  interest_region <- samples > threshold\n",
    "  \n",
    "  list(\n",
    "    name = \"One-sided Minimal Effect Test\",\n",
    "    null = paste0(\"π ≤ \", threshold),\n",
    "    interest = paste0(\"π > \", threshold),\n",
    "    p_null = sum(null_region) / length(samples),\n",
    "    p_interest = sum(interest_region) / length(samples),\n",
    "    threshold = threshold\n",
    "  )\n",
    "}\n",
    "\n",
    "# 等价性检验（与 ROPE Test 数学相同，语义一致，可选保留）\n",
    "equivalence_test <- function(samples, rope_lower = 0.4, rope_upper = 0.6) {\n",
    "  null_region <- samples <= rope_lower | samples >= rope_upper\n",
    "  interest_region <- samples > rope_lower & samples < rope_upper\n",
    "  \n",
    "  list(\n",
    "    name = \"Equivalence Test\",\n",
    "    null = paste0(\"π ≤ \", rope_lower, \" or π ≥ \", rope_upper),\n",
    "    interest = paste0(rope_lower, \" < π < \", rope_upper),\n",
    "    p_null = sum(null_region) / length(samples),\n",
    "    p_interest = sum(interest_region) / length(samples),\n",
    "    rope_lower = rope_lower,\n",
    "    rope_upper = rope_upper\n",
    "  )\n",
    "}\n",
    "\n",
    "# 非劣性检验: H0: π < 0.4 vs H1: π ≥ 0.4\n",
    "non_inferiority_test <- function(samples, threshold = 0.4) {\n",
    "  null_region <- samples < threshold\n",
    "  interest_region <- samples >= threshold\n",
    "  \n",
    "  list(\n",
    "    name = \"Non-inferiority Test\",\n",
    "    null = paste0(\"π < \", threshold),\n",
    "    interest = paste0(\"π ≥ \", threshold),\n",
    "    p_null = sum(null_region) / length(samples),\n",
    "    p_interest = sum(interest_region) / length(samples),\n",
    "    threshold = threshold\n",
    "  )\n",
    "}\n",
    "\n",
    "# ============================================\n",
    "# 3. 执行所有检验 \n",
    "# ============================================\n",
    "\n",
    "results <- list(\n",
    "  rope_test(pi_posterior, rope_lower = 0.4, rope_upper = 0.6),\n",
    "  one_sided_nhst(pi_posterior, null_val = 0.5),\n",
    "  two_sided_met(pi_posterior, rope_lower = 0.4, rope_upper = 0.6),\n",
    "  one_sided_met(pi_posterior, threshold = 0.6),\n",
    "  equivalence_test(pi_posterior, rope_lower = 0.4, rope_upper = 0.6),\n",
    "  non_inferiority_test(pi_posterior, threshold = 0.4)\n",
    ")\n",
    "\n",
    "\n",
    "# ============================================\n",
    "# 4. 可视化函数\n",
    "# ============================================\n",
    "\n",
    "visualize_test_pi <- function(samples, test_result, xlim = c(0, 1)) {\n",
    "  df <- data.frame(pi = samples)\n",
    "  \n",
    "  p <- ggplot(df, aes(x = pi)) +\n",
    "    geom_density(fill = \"gray80\", alpha = 0.5) +\n",
    "    geom_vline(xintercept = 0.5, linetype = \"dashed\", color = \"black\", linewidth = 0.8) +\n",
    "    labs(\n",
    "      title = test_result$name,\n",
    "      subtitle = paste0(\"Null: \", test_result$null, \" | Interest: \", test_result$interest),\n",
    "      x = \"Parameter π\",\n",
    "      y = \"Posterior Density\"\n",
    "    ) +\n",
    "    theme_minimal() +\n",
    "    theme(\n",
    "      plot.title = element_text(face = \"bold\", size = 11),\n",
    "      plot.subtitle = element_text(size = 9),\n",
    "      axis.title = element_text(size = 10)\n",
    "    ) +\n",
    "    xlim(xlim)\n",
    "  \n",
    "  # 添加区间标注\n",
    "  if (test_result$name == \"ROPE Test (Practical Equivalence)\" || \n",
    "      test_result$name == \"Equivalence Test\") {\n",
    "    p <- p +\n",
    "      annotate(\"rect\", xmin = test_result$rope_lower, xmax = test_result$rope_upper,\n",
    "               ymin = 0, ymax = Inf, alpha = 0.2, fill = \"blue\") +\n",
    "      geom_vline(xintercept = c(test_result$rope_lower, test_result$rope_upper),\n",
    "                 linetype = \"dotted\", color = \"blue\", linewidth = 0.8)\n",
    "    \n",
    "  } else if (test_result$name == \"Two-sided Minimal Effect Test\") {\n",
    "    p <- p +\n",
    "      annotate(\"rect\", xmin = test_result$rope_lower, xmax = test_result$rope_upper,\n",
    "               ymin = 0, ymax = Inf, alpha = 0.2, fill = \"red\") +\n",
    "      geom_vline(xintercept = c(test_result$rope_lower, test_result$rope_upper),\n",
    "                 linetype = \"dotted\", color = \"red\", linewidth = 0.8)\n",
    "    \n",
    "  } else if (test_result$name == \"One-sided Minimal Effect Test\") {\n",
    "    p <- p +\n",
    "      geom_vline(xintercept = test_result$threshold,\n",
    "                 linetype = \"dotted\", color = \"red\", linewidth = 0.8)\n",
    "    \n",
    "  } else if (test_result$name == \"Non-inferiority Test\") {\n",
    "    p <- p +\n",
    "      geom_vline(xintercept = test_result$threshold,\n",
    "                 linetype = \"dotted\", color = \"blue\", linewidth = 0.8)\n",
    "    \n",
    "  } else if (test_result$name == \"One-sided NHST\") {\n",
    "    p <- p +\n",
    "      geom_vline(xintercept = test_result$null_val,\n",
    "                 linetype = \"dotted\", color = \"black\", linewidth = 0.8)\n",
    "  }\n",
    "  \n",
    "  return(p)\n",
    "}\n",
    "\n",
    "# 生成图形\n",
    "plots <- lapply(results, function(r) visualize_test_pi(pi_posterior, r))\n",
    "\n",
    "# 组合图形（2列）\n",
    "do.call(grid.arrange, c(plots, ncol = 2))\n",
    "\n",
    "\n",
    "# ============================================\n",
    "# 5. ROPE、HDI、后验摘要\n",
    "# ============================================\n",
    "\n",
    "# 使用 bayestestR 的 rope() 函数验证（ROPE = [0.4, 0.6]）\n",
    "rope_bayestestR <- rope(pi_posterior, range = c(0.4, 0.6), ci = 0.95)\n",
    "cat(\"\\n=== bayestestR ROPE Analysis (95% CI) ===\\n\")\n",
    "print(rope_bayestestR)\n",
    "\n",
    "# 95% HDI\n",
    "hdi_result <- hdi(pi_posterior, ci = 0.95)\n",
    "cat(\"\\n95% Highest Density Interval (HDI):\", \n",
    "    round(hdi_result$CI_low, 4), \"to\", round(hdi_result$CI_high, 4), \"\\n\")\n",
    "\n",
    "# 后验均值与中位数\n",
    "cat(\"Posterior Mean of π:\", round(mean(pi_posterior), 4), \"\\n\")\n",
    "cat(\"Posterior Median of π:\", round(median(pi_posterior), 4), \"\\n\")\n",
    "\n",
    "# 判断是否等效：如果 HDI 完全在 [0.4, 0.6] 内，则 strong evidence for equivalence\n",
    "hdi_in_rope <- hdi_result$CI_low > 0.4 & hdi_result$CI_high < 0.6\n",
    "cat(\"HDI fully within ROPE [0.4, 0.6]?\", ifelse(hdi_in_rope, \"YES\", \"NO\"), \"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "<h2>3. 基于贝叶斯因子的统计推断</h2><p>贝叶斯假设检验的另一个取向：贝叶斯因子 (Bayes factor, BF)</p><p></p><p><strong>假设检验 vs. 贝叶斯因子</strong></p><p>在传统假设检验中，我们会计算出一个 $ p $ 值。如果 $ p $ 值小于等于设定的显著性水平（例如 0.05），则拒绝零假设，认为自我和他人条件下的反应时存在显著差异。</p><p></p><img src=\"https://cdn.kesci.com/upload/smw4sakmzz.png?imageView2/0/w/320/h/960\" alt=\"Image Name\"><p>与传统的假设检验方法不同，贝叶斯统计使用 <strong>贝叶斯因子（Bayes Factor，BF）</strong> 来衡量不同模型之间的相对证据强度。贝叶斯因子不是基于 $ p $ 值，而是通过比较模型间的后验概率来得出结论。</p><p></p><p><strong>基本概念</strong></p><p>频率学派将随机事件发生的频率作为一种客观指标，而贝叶斯学派则从观察者的视角出发将概率理解为一种主观不确定性。</p><p></p><p>贝叶斯因子（Bayes Factor，BF）作为一种基于贝叶斯统计的验证方法，主要用于比较零假设（$ H_0 $）与备择假设（$ H_1 $）的相对支持程度，其衡量的主要是数据在这两种假设下的解释能力。</p><p></p><p>具体来说，贝叶斯因子可以表示为：</p><p>$$ \\begin{align*} \\text{Bayes Factor} &amp;= \\frac{\\text{posterior odds }}{\\text{prior odds }} \\\\ &amp;= \\frac{\\text{后验概率比}}{\\text{先验概率比}} \\\\ &amp;= \\frac{P(H_1 | Y) / P(H_0 | Y)}{P(H_1) / P(H_0)} \\end{align*} $$</p><p></p><ul><li><p>Posterior odds：后验概率比</p></li><li><p>Prior odds：先验概率比</p></li><li><p>$ H_0 $：零假设</p></li><li><p>$ H_1 $：备择假设</p></li></ul><p></p><blockquote><p>Heck, D. W., Boehm, U., Böing-Messing, F., Bürkner, P.-C., Derks, K., Dienes, Z., Fu, Q., Gu, X., Karimova, D., Kiers, H. A. L., Klugkist, I., Kuiper, R. M., Lee, M. D., Leenders, R., Leplaa, H. J., Linde, M., Ly, A., Meijerink-Bosman, M., Moerbeek, M., … Hoijtink, H. (2023). A review of applications of the bayes factor in psychological research. Psychological Methods, 28(3), 558–579. <a target=\"_blank\" rel=\"noopener noreferrer nofollow\" href=\"https://doi.org/10.1037/met0000454\">https://doi.org/10.1037/met0000454</a></p></blockquote><p></p>"
   ]
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  {
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   "source": [
    "<p>当然，贝叶斯因子还有一种表达方式，即后验概率比等于贝叶斯因子乘以先验概率比：</p><p>$$ \\begin{align*} \\text{posterior odds} &amp;= \\text{BF}_{10} \\times \\text{prior odds} \\end{align*} $$</p><p>这说明，贝叶斯因子反映了数据对假设的支持程度，也反映了先验概率到后验概率变化的程度或证据。</p>"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "<p>同时，贝叶斯因子分析能够帮助研究者根据现有证据评估不同假设成立的可能性之比，并且在评估证据强度上也有一套独立的标准：</p><table style=\"min-width: 50px;\"><colgroup><col style=\"min-width: 25px;\"><col style=\"min-width: 25px;\"></colgroup><tbody><tr><th colspan=\"1\" rowspan=\"1\"><p><strong>贝叶斯因子</strong></p></th><th colspan=\"1\" rowspan=\"1\"><p><strong>解读</strong></p></th></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>&gt; 100</p></td><td colspan=\"1\" rowspan=\"1\"><p>极强的证据支持$ H_1 $</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>30 ~ 100</p></td><td colspan=\"1\" rowspan=\"1\"><p>非常强的证据支持$ H_1 $</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>10 ~ 30</p></td><td colspan=\"1\" rowspan=\"1\"><p>较强的证据支持$ H_1 $</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>3 ~ 10</p></td><td colspan=\"1\" rowspan=\"1\"><p>中等程度的证据支持$ H_1 $</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>1 ~ 3</p></td><td colspan=\"1\" rowspan=\"1\"><p>较弱的证据支持$ H_1 $</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>1</p></td><td colspan=\"1\" rowspan=\"1\"><p>没有证据</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>1/3 ~ 1</p></td><td colspan=\"1\" rowspan=\"1\"><p>较弱的证据支持$ H_0 $</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>1/10 ~ 1/3</p></td><td colspan=\"1\" rowspan=\"1\"><p>中等程度的证据支持$ H_0 $</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>1/30 ~ 1/10</p></td><td colspan=\"1\" rowspan=\"1\"><p>较强的证据支持$ H_0 $</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>1/100 ~ 1/30</p></td><td colspan=\"1\" rowspan=\"1\"><p>非常强的证据支持$ H_0 $</p></td></tr><tr><td colspan=\"1\" rowspan=\"1\"><p>&lt; 1/100</p></td><td colspan=\"1\" rowspan=\"1\"><p>极强的证据支持$ H_0 $</p></td></tr></tbody></table><blockquote><p>Source: 该表改编自胡传鹏等(2018)，源引用于Lee &amp; Wagenmakers (2014)。</p></blockquote><p></p><p></p><ul><li><p>$ BF_{10} $ = 1，收集到的数据并没有改变备择假设$ H_1 $的相对可能性</p></li><li><p>$ BF_{10} $ &gt; 1，收集到的数据增加了备择假设$ H_1 $的相对可能性。$ BF $越大，表明支持备择假设$ H_1 $的证据越强</p></li><li><p>$ BF_{10} $ &lt; 1，收集到的数据削弱了备择假设$ H_1 $的相对可能性。$ BF $越小，表明支持备择假设$ H_1 $的证据越弱</p></li></ul><p></p><blockquote><p>胡传鹏, 孔祥祯, Eric-Jan Wagenmakers, Alexander Ly, 彭凯平. (2018). 贝叶斯因子及其在JASP中的实现. <em>心理科学进展</em></p></blockquote><blockquote><p>Makowski, D., Ben-Shachar, M. S., &amp; Lüdecke, D. (2019). bayestestR: Describing Effects and their Uncertainty, Existence and Significance within the Bayesian Framework. Journal of Open Source Software, 4(40), 1541. <a target=\"_blank\" rel=\"noopener noreferrer nofollow\" href=\"https://doi.org/10.21105/joss.01541\">https://doi.org/10.21105/joss.01541</a></p></blockquote><blockquote><p>Makowski, D., Ben-Shachar, M. S., Chen, S. H. A., &amp; Lüdecke, D. (2019). Indices of Effect Existence and Significance in the Bayesian Framework. Retrieved from 10.3389/fpsyg.2019.02767</p></blockquote><p></p>"
   ]
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  {
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   "source": [
    "<p>贝叶斯因子非常灵活，因为它不仅可以用于简单的假设检验，还可以用于比较复杂模型、评估模型拟合优度、以及在多模型比较中提供更丰富的信息。</p><p></p><p><strong>贝叶斯因子同样可以应用于以下三种常见的假设检验方法：</strong></p><p></p><ol><li><p><strong>Testing against the point-null</strong></p><p>贝叶斯因子可以用来检验某个参数是否等于零，即检验点的零假设。</p></li></ol><p></p><ol start=\"2\"><li><p><strong>Testing against a null-region</strong></p></li></ol><p>设定一个“零区域”，即一个参数值的范围，该范围内的值被认为与零没有显著差异。假设我们设定一个区间 $ \\beta_1 \\in [-0.05, 0.05] $，认为 $ \\beta_1 $ 落在这个区间内是可以接受的无效效应。通过贝叶斯因子，我们可以计算数据支持 $ \\beta_1 $ 在零区域内（$ \\beta_1 \\in [-0.05, 0.05] $）或零区域外（$ \\beta_1 \\notin [-0.05, 0.05] $）的证据强度。</p><p></p><ol start=\"3\"><li><p><strong>Directional hypotheses</strong></p></li></ol><p>即是否存在正向或负向的影响。例如，我们可以提出假设 $ H_1: \\beta_1 &gt; 0 $，认为自变量 （Label）对因变量（RT_sec）有正向影响。贝叶斯因子将帮助我们评估数据是否支持这种方向性的假设，而不仅仅是支持或拒绝零假设。</p><p></p>"
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   "source": [
    "<p>我们还是前述的Beta-Binomial模型为例</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "<p></p><p><strong>模型假设</strong></p><ul><li><p>判断正确概率 $ \\pi $ 服从 <strong>Beta 分布</strong>分布：</p></li></ul><p>$$ \\begin{equation} \\pi \\sim \\text{Beta}(\\alpha, \\beta) \\end{equation} $$</p><ul><li><p>在每次试验中，参与者的成功次数 $ Y $ 服从 <strong>Binomial 分布</strong>：</p></li></ul><p>$$ \\begin{equation} Y \\sim \\text{Binomial}(n, \\pi) \\end{equation} $$</p><p>其中，$ n $是试验的总次数，$ Y $是成功次数。</p><p></p><p><strong>模型设定</strong></p><p>在这个例子中，我们可以使用Beta-Binomial 模型来表示：</p><p></p><blockquote><p>数据: 总试验数为n=118，成功次数为99 $ (Y = 99) $<br>先验分布为：$ \\pi \\sim \\text{Beta}(2, 2) $<br>似然函数为：$ Y|\\pi \\sim \\text{Bin}(n=118, \\pi) $</p></blockquote><p></p>"
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     "text": [
      "Inference for Stan model: anon_model.\n",
      "4 chains, each with iter=5000; warmup=1000; thin=1; \n",
      "post-warmup draws per chain=4000, total post-warmup draws=16000.\n",
      "\n",
      "   mean se_mean   sd 2.5%  25%  50%  75% 97.5% n_eff Rhat\n",
      "pi 0.83       0 0.03 0.76 0.81 0.83 0.85  0.89  6080    1\n",
      "\n",
      "Samples were drawn using NUTS(diag_e) at Fri Nov  7 08:24:36 2025.\n",
      "For each parameter, n_eff is a crude measure of effective sample size,\n",
      "and Rhat is the potential scale reduction factor on split chains (at \n",
      "convergence, Rhat=1).\n"
     ]
    }
   ],
   "source": [
    "print(fit_bb, pars = c(\"pi\"))"
   ]
  },
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   "source": [
    "**MCMC诊断**"
   ]
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IF1OH6ozGtnoZ8PiuzBv5DNkH3s5iFuQErQsUgYjjWXyMkHobMi7AWEUPgFKbtq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CKpNiClGVZph6hIw/KtO8ToE4RMAkILsJ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\nA6E6XB5ZAhQdimdgZjatx0CDTi2HLoKO6a8lWWmGbPMYKa/GG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ySkvmtvKmtW9aC23Q6yyRjUE2Z1sXKwC/bmRBThQqHDsQ4C0CFeVDH8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\nSHhpGEFAES9CgSuohSKcgQDBZ9RitUKlX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VRLgF6d7zghArSpVE5FqPDsTvoSmNY/iXAIszuZOM4U3yhP3Uik9+zsTi5OEftmc4TTx3Ft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\nYmoKc3RhcnR4cmVmCjExMjE5NgolJUVPRgo=",
      "text/html": [
       "<img src=\"https://cdn.kesci.com/upload/rt/6FF53CE8326049C99ABF1D227BB8F780/t5ckr3cq8l.svg\">"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "application/pdf": {
       "height": 420,
       "width": 420
      },
      "image/jpeg": {
       "height": 420,
       "width": 420
      },
      "image/png": {
       "height": 420,
       "width": 420
      },
      "image/svg+xml": {
       "height": 420,
       "isolated": true,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "trace_pi <- bayesplot::mcmc_trace(\n",
    "  fit_bb,\n",
    "  pars = \"pi\"\n",
    ") +\n",
    "  papaja::theme_apa()\n",
    "\n",
    "trace_pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "30568BD553E648A3996F78AD26DB9DF8",
    "jupyter": {},
    "notebookId": "690a86a8ae50d8e7fdf63a45",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "<h3>3.1 Testing against the point-null</h3><p>贝叶斯因子可以帮助我们衡量数据对点零假设与非零假设的支持程度。在Beta-Binomial模型中，我们可以设定一个零假设 $ H_0: \\pi = 0.5 $ 和备择假设 $ H_1: \\pi \\neq 0.5 $，然后使用贝叶斯因子来计算零假设和备择假设的相对证据。</p><p>$$ BF_{10} = \\frac{P(\\text{Data} | H_1)}{P(\\text{Data} | H_0)} = \\frac{P(Data|\\pi \\neq 0.5)}{P(Data|\\pi = 0.5)} $$</p><p></p><p>其中，$ P(Data | H_1) $ 和 $ P(Data | H_0) $ 分别表示在备择假设$ H_1 $和零假设$ H_0 $下数据的似然值。</p><p></p><p><strong>实现贝叶斯因子计算</strong></p><p>现在，我们有了 $ \\beta_1 $ 的先验分布和后验分布，我们分别计算贝叶斯因子 $ BF_{10} $ 和 $ BF_{01} $，以表示数据支持备择假设和零假设的证据强度，并且通过直接计算贝叶斯因子的方法，对先验和后验分布在零假设点处的概率密度值进行可视化。</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "hide_input": false,
    "id": "1CFDDDCD53F445E3950F666BA1AC5D59",
    "jupyter": {},
    "notebookId": "690a86a8ae50d8e7fdf63a45",
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": [],
    "trusted": true,
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).\n",
      "Chain 1: \n",
      "Chain 1: Gradient evaluation took 7e-06 seconds\n",
      "Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.07 seconds.\n",
      "Chain 1: Adjust your expectations accordingly!\n",
      "Chain 1: \n",
      "Chain 1: \n",
      "Chain 1: Iteration:    1 / 5000 [  0%]  (Warmup)\n",
      "Chain 1: Iteration:  500 / 5000 [ 10%]  (Warmup)\n",
      "Chain 1: Iteration: 1000 / 5000 [ 20%]  (Warmup)\n",
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     ]
    }
   ],
   "source": [
    "# =====================================\n",
    "# 从先验采样（无数据似然）\n",
    "# =====================================\n",
    "# 定义模型\n",
    "stan_prior_code <- \"\n",
    "data {\n",
    "  int<lower=0> N;       \n",
    "  int<lower=0, upper=N> Y; \n",
    "}\n",
    "parameters {\n",
    "  real<lower=0, upper=1> pi;\n",
    "}\n",
    "model {\n",
    "  pi ~ beta(2, 2);\n",
    "  \n",
    "  // 注释掉似然\n",
    "  // Y ~ binomial(N, pi);\n",
    "}\n",
    "\"\n",
    "\n",
    "# 编译先验模型\n",
    "prior_model <- stan_model(model_code = stan_prior_code)\n",
    "\n",
    "# 从先验采样（使用虚拟数据）\n",
    "fit_prior <- sampling(\n",
    "  prior_model,\n",
    "  data = stan_data,  # 虚拟\n",
    "  iter = 5000,\n",
    "  warmup = 1000,\n",
    "  chains = 4,\n",
    "  seed = 84735\n",
    ")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "runtime": {
     "execution_status": null,
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     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
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    "tags": []
   },
   "source": [
    "<p><strong>🔍 Savage-Dickey 公式来源</strong></p><p>Savage-Dickey 密度比的标准形式是（见 Wagenmakers et al., 2010）：</p><p>$$ \\text{BF}_{01} = \\frac{p(\\beta_1 = 0 \\mid \\text{data}, \\mathcal{M}_1)}{p(\\beta_1 = 0 \\mid \\mathcal{M}_1)} $$</p><p>其中：</p><ul><li><p>分子 p(β₁=0 | data, M₁)： 表示在备择模型 M₁（即包含参数β₁的模型）下的已经观察到数据之后，参数β₁在零点（原假设H₀指定的点）的后验密度。它衡量了在看到数据后，我们认为β₁等于0的可能性有多大。</p></li><li><p>分母 p(β₁=0 | M₁)： 表示在备择模型 M₁下的看到任何数据之前，参数β₁在零点的先验密度。它衡量了在看到数据之前，我们认为β₁等于0的可能性有多大。</p></li><li><p>BF₀₁： 是支持<strong>原假设（M₀）</strong> 相对于<strong>备择假设（M₁）</strong> 的证据。<strong>BF₀₁的值越大，证据越支持原假设（即β₁=0）</strong>。</p></li></ul><p></p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
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    "id": "CA19BCFA685C4833A102F850996ABC4F",
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   "source": [
    "# 提取pi的先验样本\n",
    "prior_samples <- extract(fit_prior)\n",
    "pi_prior <- prior_samples$`pi`\n",
    "\n",
    "# 提取后验样本\n",
    "posterior_samples <- extract(fit_bb)\n",
    "pi_posterior <- posterior_samples$`pi`\n",
    "\n",
    "# 计算贝叶斯因子\n",
    "\n",
    "# 使用核密度估计计算密度在 0.5 处的值\n",
    "prior_density <- density(pi_prior, from = 0.49, to = 0.51, n = 1024)\n",
    "posterior_density <- density(pi_posterior, from = 0.49, to = 0.51, n = 1024)\n",
    "\n",
    "# 找到最接近 0 的点的密度值\n",
    "idx_0_prior <- which.min(abs(prior_density$x))\n",
    "idx_0_post <- which.min(abs(posterior_density$x))\n",
    "\n",
    "prior_at_0 <- prior_density$y[idx_0_prior]\n",
    "# posterior 太小，设置为0.0001，避免出现无穷大\n",
    "posterior_at_0 <- if_else(posterior_density$y[idx_0_post] ==0, 0.0001, posterior_density$y[idx_0_post])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
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    "id": "47D326F5155840A4BF963878537A0883",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " num [1:16000(1d)] 0.815 0.848 0.849 0.817 0.802 ...\n",
      " - attr(*, \"dimnames\")=List of 1\n",
      "  ..$ iterations: NULL\n"
     ]
    }
   ],
   "source": [
    "str(pi_posterior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "id": "2906F0BEB8854F799F38DB78E3118116",
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " num [1:16000(1d)] 0.811 0.338 0.687 0.299 0.178 ...\n",
      " - attr(*, \"dimnames\")=List of 1\n",
      "  ..$ iterations: NULL\n"
     ]
    }
   ],
   "source": [
    "str(pi_prior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "id": "38E9E1491C384D0FAEB7AEF54EC1F296",
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    "notebookId": "690a86a8ae50d8e7fdf63a45",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The BF_10 is 14583.88 \n",
      "The BF_01 is 6.9e-05 \n"
     ]
    }
   ],
   "source": [
    "# 计算 Savage-Dickey 比\n",
    "BF_01 <- posterior_at_0 / prior_at_0# 支持 H0 相对于 H1\n",
    "BF_10 <- 1 / BF_01# 支持 H1（β₁ ≠ 0）相对于 H0（β₁ = 0）\n",
    "\n",
    "\n",
    "cat(\"The BF_10 is\", round(BF_10, 2), \"\\n\")\n",
    "cat(\"The BF_01 is\", round(BF_01, 6), \"\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
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   "outputs": [
    {
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Ui3JEI3d3JAP6QYXmnH1mJQanJ5ijEQ8TrKcgxMctbQZkEGIiskG1ThcKRtrMjA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\ntM+FdQx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      "text/html": [
       "<img src=\"https://cdn.kesci.com/upload/rt/7F5A3BCDEE2F48F3B225FE1E1805399C/t5cktwp4p.svg\">"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "application/pdf": {
       "height": 420,
       "width": 420
      },
      "image/jpeg": {
       "height": 420,
       "width": 420
      },
      "image/png": {
       "height": 420,
       "width": 420
      },
      "image/svg+xml": {
       "height": 420,
       "isolated": true,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 提取pi的先验和后验样本\n",
    "prior_samples <- extract(fit_prior)\n",
    "pi_prior <- prior_samples$`pi`\n",
    "\n",
    "posterior_samples <- extract(fit_bb)\n",
    "pi_posterior <- posterior_samples$`pi`\n",
    "\n",
    "\n",
    "\n",
    "prior_density <- density(pi_prior, from = min(c(pi_prior, pi_posterior)), \n",
    "                        to = max(c(pi_prior, pi_posterior)), n = 1024)\n",
    "posterior_density <- density(pi_posterior, from = min(c(pi_prior, pi_posterior)), \n",
    "                            to = max(c(pi_prior, pi_posterior)), n = 1024)\n",
    "\n",
    "# 准备绘图数据\n",
    "df_prior <- data.frame(\n",
    "  pi = prior_density$x,\n",
    "  density = prior_density$y,\n",
    "  type = \"Prior\"\n",
    ")\n",
    "\n",
    "df_posterior <- data.frame(\n",
    "  pi = posterior_density$x,\n",
    "  density = posterior_density$y,\n",
    "  type = \"Posterior\"\n",
    ")\n",
    "\n",
    "df_combined <- bind_rows(df_prior, df_posterior)\n",
    "\n",
    "\n",
    "# 主密度图\n",
    "main_plot <- ggplot(df_combined, aes(x = pi, y = density, color = type)) +\n",
    "  geom_line(size = 1.2, alpha = 0.8) +\n",
    "  scale_color_manual(values = c(\"Prior\" = \"steelblue\", \"Posterior\" = \"darkorange\")) +\n",
    "  labs(\n",
    "    title = \"Prior and Posterior Distribution Comparison\",\n",
    "    x = expression(pi),\n",
    "    y = \"Density\",\n",
    "    color = \"Distribution\"\n",
    "  ) +\n",
    "  theme_minimal() +\n",
    "  theme(\n",
    "    legend.position = c(0.85, 0.85),\n",
    "    plot.title = element_text(hjust = 0.5, face = \"bold\"),\n",
    "    panel.grid.minor = element_blank()\n",
    "  )\n",
    "\n",
    "# 添加分面版本以更好比较分布特性\n",
    "facet_plot <- ggplot(df_combined, aes(x = pi, y = density, fill = type)) +\n",
    "  geom_area(alpha = 0.6) +\n",
    "  facet_wrap(~ type, ncol = 1, scales = \"free_y\") +\n",
    "  scale_fill_manual(values = c(\"Prior\" = \"steelblue\", \"Posterior\" = \"darkorange\")) +\n",
    "  labs(x = expression(pi), y = \"Density\") +\n",
    "  theme_minimal() +\n",
    "  theme(legend.position = \"none\")\n",
    "\n",
    "# 组合图形\n",
    "combined_plot <- main_plot / facet_plot +\n",
    "  plot_annotation(title = \"Bayesian Analysis: Prior vs Posterior Distributions\",\n",
    "                  theme = theme(plot.title = element_text(hjust = 0.5, face = \"bold\")))\n",
    "\n",
    "print(combined_plot)"
   ]
  },
  {
   "cell_type": "markdown",
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    "id": "8080E0FF93B142A4BA51ACBBE545973B",
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    "runtime": {
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   "source": [
    "<p>通过上图我们可以发现：</p><ol><li><p>$ BF_{10} = 14536.01 $：表示数据支持$ H_1 $的强度相对于$ H_0 $设为 14536.01 。</p></li><li><p>$ BF_{01} =6.9e-05  $：表示数据支持$ H_0 $的强度相对于$ H_1 $为 6.9e-05 。</p></li></ol><p>总结：通过贝叶斯因子的计算，对于数据倾向于支持 $ \\beta_1 \\neq 0 $，即存在效应提供了极强（&gt;100)的证据。</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "F305C1F754784D1184DB5147EB6C2F89",
    "jupyter": {},
    "notebookId": "690a86a8ae50d8e7fdf63a45",
    "runtime": {
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    },
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   "source": [
    "<p><strong>与 JASP 的对比</strong></p><p>在上一小节，我们通过直接比较先验和后验分布在零点的密度差异来检验某个效应是否为零。</p><p>然而，JASP（Jeffreys's Amazing Statistics Program）提供了一种不同的方法来计算贝叶斯因子：</p><ul><li><p>JASP 是一个基于 R 语言的开源软件，以其易用性和友好的图形界面广受欢迎，主要用于心理学、社会学等领域的统计分析。</p></li><li><p>JASP 使用贝叶斯模型来计算贝叶斯因子，包括模型比较和桥采样法（Bridge Sampling）等技术，能够通过计算后验和先验分布的比值，评估不同模型或假设的相对支持程度。与 Savage-Dickey 方法不同，桥采样不局限于单参数或简单假设，因此更适合模型比较和复杂假设检验。</p></li></ul><p></p><p><strong>注意：由于这里的方法基于模型比较，它更适合模型比较和复杂假设检验，因此和 Savage-Dickey 方法不同。此外，在JASP的实际运算中，软件会自动调整先验，因此与我们设置的先验不同，计算得到的贝叶斯因子也会有所不同。</strong></p><p></p><img src=\"https://cdn.kesci.com/upload/1762414215845_1.jpg\"><p></p>"
   ]
  },
  {
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   "metadata": {
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    "<img src=\"https://cdn.kesci.com/upload/1762414056164_1.jpg\"><p></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "37434ED98C544A9FAAD91787B7F546EA",
    "jupyter": {},
    "notebookId": "690a86a8ae50d8e7fdf63a45",
    "runtime": {
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   "source": [
    "<h3>3.2 Testing against a null-region</h3><p>现在，我们证实了$ \\pi \\neq 0.5 $，即正确率不为0.5.</p><p></p><p><strong>回顾 ROPE</strong></p><ul><li><p>假设了 $ \\pi$ 的值在 $ [0.4, 0.6] $ 范围内可以视为实用等效区间，也就是说，</p></li><li><p>如果 $ \\pi $ 落在这个区间内，我们可以认为正确率为0.5，从而在实践上认为两者无显著差异。</p></li></ul><p></p><p><strong>ROPE 对于贝叶斯因子的意义</strong></p><ul><li><p>在假设检验中，设定一个“零区域”（null region）可以帮助我们定义一个在实际意义上视为“无效”的效果范围。</p></li><li><p>通过设定零区域，<strong>我们可以计算先验概率和后验概率，进而计算贝叶斯因子来量化数据对假设的支持强度</strong>。</p></li></ul><p>$$ BF_{10} = \\frac{P(\\text{Data} | H_1)}{P(\\text{Data} | H_0)} = \\frac{P(Data|\\beta_1 \\notin [0.4,0.6])}{P(Data|\\beta_1 \\in [0.4,0.6])} $$</p><p>（注：我们可以计算 \"label\" 条件下反应时间差异落在零假设区间之外的先验概率，以及落在零假设区间之内的先验概率，从而得到我们的先验概率比（prior odds）。）</p><p></p>"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "<p><strong>贝叶斯因子的计算</strong></p><p>首先，我们需要确定 $ \\pi $ 在 ROPE 范围 $ (0.4, 0.6) $ 内的概率，即：</p><p>$$ \\begin{align*} P(H0|Y) &amp;= P(0.4 \\leq \\pi \\leq 0.6 | Y) = \\int_{0.4}^{0.6} f(\\pi | Y) d\\pi \\\\ \\end{align*} $$</p><ul><li><p>其中 $ f(\\pi | Y) $ 是 $ \\pi $ 的后验密度函数。根据我们的后验分布 $ Beta(101, 21) $，我们可以使用积分或数值方法来求解具体数值。</p></li></ul><p>与此同时，我们考虑 $ (0.4, 0.6) $ 之外的概率，即 $ P(\\pi \\notin (0.4, 0.6) | Y) $，通过：</p><p>$$ P(H1|Y) = P(\\pi \\notin (0.4, 0.6) | Y) = 1 - P(H0|Y) $$</p><p>现在我们可以根据下式计算贝叶斯因子（BF）：</p><p>$$ \\text{Bayes Factor } = \\frac{P(0.4 \\leq \\pi \\leq 0.6 | Y)/P(H0)}{P(\\pi \\notin (0.4, 0.6) | Y)/P(H1)} $$</p><p><strong>由于两种假设下先验分布相同，$ P(H0) = P(H1) = 0.5 $，因此可以简化计算为：</strong></p><p>$$ \\text{Bayes Factor } = \\frac{P(0.4 \\leq \\pi \\leq 0.6 | Y)}{P(\\pi \\notin (0.4, 0.6) | Y)} $$</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0409684F65BC4FE9970417423529B3D5",
    "jupyter": {},
    "notebookId": "690a86a8ae50d8e7fdf63a45",
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   "source": [
    "<p><strong>结果分析</strong></p><p>计算 $ P(0.4 \\leq \\pi \\leq 0.6 | Y) $ 可以用$ Beta $分布的累积分布函数（CDF）进行:</p><p>$$ P(0.4 \\leq \\pi \\leq 0.6 | Y) = F(0.6) - F(0.4) $$</p><ul><li><p>其中 $ F $ 是以 $ Beta $ 分布(101,21)累积分布函数。则，</p></li></ul><p>$$ P(0.4 \\leq \\pi \\leq 0.6 | Y) \\approx 0.022 - 0.0003 = 0.0217 $$</p><p>因此，$ P(\\pi \\notin (0.4, 0.6) | Y) = 1 - 0.0217 = 0.9783 $。</p><p>计算贝叶斯因子（BF）:</p><p>$$ \\text{Bayes Factor} = \\frac{P(0.4 \\leq \\pi \\leq 0.6 | Y)}{P(\\pi \\notin (0.4, 0.6) | Y)} \\approx \\frac{0.0217}{0.9783} \\approx 0.0222 $$</p><p>贝叶斯因子的值约为 $ 0.0222 $，这意味着备择假设 $ H_1 $ ($ \\pi $ 不在 $ (0.4, 0.6) $ 区间内) 相对于原假设 $ H_0 $ ($ \\pi $ 在 $ (0.4, 0.6) $ 区间内) 获得了极大的支持。这个结果表明，给定数据和先验信息，$ \\pi $ 值显著不在 $ (0.4, 0.6) $ 区间内，大大倾向于 $ \\pi $ 的真实值远离 $ 0.5 $，这与 $ \\pi = 0.8 $ 的假设一致。</p><p>因此，我们可以结论认为，在给定的统计模型和数据条件下，成功率 $ \\pi = 0.8 $ 是显著高于一般随机判断水平（$ 0.5 $），这进一步强化了 $ \\pi $ 显著高于 $ 0.5 $ 的结论。此结果对于决策支持和进一步的统计分析具有重要意义。</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "F5B4C750C20143E9B4B5338F9CA66BC9",
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   },
   "source": [
    "<p>🙋<strong>Question</strong></p><p>如何利用我们已经得到的后验分布计算上述BF值？</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "32B392711C7143D68E5FF8ADDF0DCAE4",
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    "notebookId": "690a86a8ae50d8e7fdf63a45",
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   "source": [
    "<p><strong>练习1</strong>：</p><p></p><p>首先，可以写出“伪代码”作为计算的思路：</p><p></p><p>第一步：</p><p></p><p>每二步：</p><p></p><p>第三步：</p><p></p><p>下面，让我们进行代码实操环节😋！</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pi的后验总样本数： 16000 \n"
     ]
    }
   ],
   "source": [
    "#第一步：后验样本提取及对应转换\n",
    "\n",
    "# 用 as.vector() 统一格式\n",
    "pi_vec <- as.vector(...)  \n",
    "# 查看总样本数（确保所有有效迭代都被包含）\n",
    "total_samples <- length(pi_vec)  \n",
    "cat(\"pi的后验总样本数：\", total_samples, \"\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "id": "7CCFF4A529B14E5281E340B2F7DCEAB8",
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    {
     "name": "stdout",
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     "text": [
      "参数 pi 落在 ROPE ( 0.4 , 0.6 ) 内的后验概率： 0 \n",
      "落在 ROPE 内的样本数： 0 \n"
     ]
    }
   ],
   "source": [
    "#第二步： 计算ROPE区间内的后验概率比\n",
    "\n",
    "# 定义 ROPE 区间\n",
    "rope_low <- ...\n",
    "rope_high <- ...\n",
    "\n",
    "# 筛选：判断每个样本是否落在 (0.4, 0.6) 内\n",
    "pi_in_rope <- (... > rope_low) & (... < rope_high)  \n",
    "\n",
    "# 计算 ROPE 内的后验概率比例\n",
    "pi_rope_prob <- mean(pi_in_rope)  \n",
    "\n",
    "# 输出结果\n",
    "cat(\"参数 pi 落在 ROPE (\", rope_low, \",\", rope_high, \") 内的后验概率：\", round(pi_rope_prob, 3), \"\\n\")\n",
    "# 可选：输出落在 ROPE 内的样本数\n",
    "#cat(\"落在 ROPE 内的样本数：\", sum(pi_in_rope), \"\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "贝叶斯因子 BF₀₁（支持 pi 在 (0.4,0.6) 内）： 0 \n"
     ]
    }
   ],
   "source": [
    "# 第三步： 计算贝叶斯因子：BF₀₁ = 支持 H₀（pi在ROPE内）的概率 / 支持 H₁（pi在ROPE外）的概率\n",
    "bf01 <- (...) / (...)  \n",
    "cat(\"贝叶斯因子 BF₀₁（支持 pi 在 (0.4,0.6) 内）：\", round(bf01, 3), \"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "A4B44963C3B447CDA1FD30D056423DFA",
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    "notebookId": "690a86a8ae50d8e7fdf63a45",
    "runtime": {
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    },
    "scrolled": false,
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   },
   "source": [
    "<h3>3.3 Directional hypotheses</h3><p>我们还可以通过Directional hypotheses 检验效应是否朝着我们预期的方向发展，计算方向假设（“单侧”）的贝叶斯因子。</p><p></p><p><strong>练习2</strong><br>思考🤔：如何通过贝叶斯因子量化支持该假设的相对证据强度呢?</p>"
   ]
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  {
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   "source": [
    "# 请直接运行，无需修改\n",
    "calculate_odds <- function(tace_samples, region = c(-0.05, 0.05)) {\n",
    "\n",
    "#计算区间 [-0.05, 0.05] 内的样本\n",
    "in_range <- tace_samples[tace_samples >= region[1] & tace_samples <= region[2]]\n",
    "\n",
    "#计算区间外的样本\n",
    "out_of_range <- tace_samples[tace_samples < region[1] | tace_samples > region[2]]\n",
    "\n",
    "#计算区间内外的比例\n",
    "P_in_range <- length(in_range) / length(tace_samples)\n",
    "P_out_of_range <- length(out_of_range) / length(tace_samples)\n",
    "\n",
    "#计算比率\n",
    "ratio <- P_out_of_range / P_in_range\n",
    "\n",
    "return(ratio)\n",
    "}\n",
    "\n",
    "plot_region <- function(samples, region = c(-0.05, 0.05), dist_type = \"Prior\") {  \n",
    "  df <- data.frame(x = samples)  \n",
    "  \n",
    "  # 计算密度用于 y 位置\n",
    "  density_data <- density(samples, n = 1024)\n",
    "  null_mask <- density_data$x >= region[1] & density_data$x <= region[2]\n",
    "  alt_mask <- !null_mask\n",
    "  \n",
    "  null_density_vals <- density_data$y[null_mask]\n",
    "  alt_density_vals <- density_data$y[alt_mask]\n",
    "  \n",
    "  # x 轴范围\n",
    "  x_range <- range(samples)\n",
    "  x_span <- diff(x_range)\n",
    "  \n",
    "  ggplot(df, aes(x = x)) +    \n",
    "    stat_density(geom = \"line\", color = \"black\", size = 1) +    \n",
    "    stat_density(      \n",
    "      geom = \"area\",      \n",
    "      data = df %>% filter(x >= region[1] & x <= region[2]),      \n",
    "      fill = \"blue\", alpha = 0.3,      \n",
    "      aes(y = ..density..)\n",
    "    ) +    \n",
    "    stat_density(      \n",
    "      geom = \"area\",      \n",
    "      data = df %>% filter(x < region[1] | x > region[2]),      \n",
    "      fill = \"yellow\", alpha = 0.3,      \n",
    "      aes(y = ..density..)\n",
    "    ) +    \n",
    "    # Null 标签\n",
    "    annotate(\"text\", \n",
    "             x = mean(region),  \n",
    "             y = if(length(null_density_vals) > 0) max(null_density_vals) * 0.6 else 0,\n",
    "             label = \"Null\", \n",
    "             color = \"blue\", \n",
    "             fontface = \"bold\",\n",
    "             size = 4) +\n",
    "    # Alternative 标签\n",
    "    annotate(\"text\", \n",
    "             x = if (abs(x_range[1]) > x_range[2]) {\n",
    "               x_range[1] + 0.15 * x_span  \n",
    "             } else {\n",
    "               x_range[2] - 0.15 * x_span  \n",
    "             },\n",
    "             y = if(length(alt_density_vals) > 0) max(alt_density_vals) * 0.6 else 0,\n",
    "             label = \"Alternative\", \n",
    "             color = \"darkorange\", \n",
    "             fontface = \"bold\",\n",
    "             size = 4) +\n",
    "    labs(      \n",
    "      title = paste0(dist_type, \" Distribution with Null Region\"),      \n",
    "      x = expression(beta[1]),      \n",
    "      y = \"Density\"    \n",
    "    ) +    \n",
    "    scale_x_continuous(limits = c(x_range[1] - 0.05 * x_span, x_range[2] + 0.05 * x_span)) +    \n",
    "    theme_minimal() +    \n",
    "    theme(plot.title = element_text(hjust = 0.5)) \n",
    "}"
   ]
  },
  {
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   "execution_count": null,
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    "#=====================================\n",
    "#      基于方向的贝叶斯因子计算\n",
    "#      自行练习\n",
    "#=====================================\n",
    "\n",
    "# 获取pi的先验分布的采样\n",
    "#pi_prior =  \n",
    "\n",
    "\n",
    "# 获取pi的后验分布的采样\n",
    "# pi_posterior = ..."
   ]
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    "# 定义区间\n",
    "# region = ...\n",
    "\n",
    "# 计算先验比\n",
    "# prior_odds = ...\n",
    "\n",
    "# 计算后验比\n",
    "# prior_odds = ...\n",
    "\n",
    "# 计算贝叶斯因子\n",
    "# BF_10 = ...\n",
    "\n",
    "cat(\"贝叶斯因子（BF_10）:\", BF_10,\"\\n\")"
   ]
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    "df_plot <- tibble(\n",
    "  prior = ...,\n",
    "  posterior = ...\n",
    ") %>%\n",
    "  pivot_longer(\n",
    "    cols = everything(),\n",
    "    names_to = \"distribution\",\n",
    "    values_to = \"pi\"\n",
    "  )\n",
    "\n",
    "# === 方向性假设：H1: pi < 0.5 ===\n",
    "h0_boundary <- 0  # H₀: pi >= 0.5\n",
    "\n",
    "# 计算最大密度用于标签定位\n",
    "dens_prior <- density(pi_prior, from = -1, to = 1)\n",
    "dens_post <- density(pi_posterior, from = -1, to = 1)\n",
    "max_dens <- max(dens_prior$y, dens_post$y)\n",
    "\n",
    "# 绘图\n",
    "ggplot(df_plot, aes(x = beta1, fill = distribution, color = distribution)) +\n",
    "  geom_density(alpha = 0.3, size = 1) +\n",
    "  \n",
    "\n",
    "  annotate(\"rect\", \n",
    "           xmin = h0_boundary, xmax = Inf,\n",
    "           ymin = -Inf, ymax = Inf,\n",
    "           fill = \"blue\", alpha = 0.2, inherit.aes = FALSE) +\n",
    "  \n",
    "  # 垂直线在 0 处（假设边界）\n",
    "  geom_vline(xintercept = 0, linetype = \"dashed\", color = \"grey\", size = 1) +\n",
    "  \n",
    "  # 标签：H₀ 在右侧，H₁ 在左侧\n",
    "  annotate(\"text\",\n",
    "           x = 0.5,  # H₀ 区域（右侧）\n",
    "           y = max_dens * 0.8,\n",
    "           label = \"H0: pi >= 0.5\",\n",
    "           color = \"blue\",\n",
    "           fontface = \"bold\",\n",
    "           size = 4,\n",
    "           parse = TRUE) +\n",
    "  \n",
    "  annotate(\"text\",\n",
    "           x = -0.5,  # H₁ 区域（左侧）\n",
    "           y = max_dens * 0.6,\n",
    "           label = \"H1: pi < 0.5\",\n",
    "           color = \"darkorange\",\n",
    "           fontface = \"bold\",\n",
    "           size = 4,\n",
    "           parse = TRUE) +\n",
    "  \n",
    "  xlim(-1, 1) +\n",
    "  \n",
    "  labs(\n",
    "    title = \"Directional Hypothesis: Testing for Negative Effect\",\n",
    "    x = expression(beta[1]),\n",
    "    y = \"Density\",\n",
    "    fill = \"Distribution\",\n",
    "    color = \"Distribution\"\n",
    "  ) +\n",
    "  \n",
    "  scale_fill_manual(values = c(\"prior\" = \"cyan\", \"posterior\" = \"coral\")) +\n",
    "  scale_color_manual(values = c(\"prior\" = \"cyan\", \"posterior\" = \"coral\")) +\n",
    "  \n",
    "  theme_minimal() +\n",
    "  theme(\n",
    "    panel.border = element_rect(fill = NA, colour = \"black\"),\n",
    "    panel.grid.minor = element_blank(),\n",
    "    legend.position = \"upper right\"\n",
    "  )"
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   "source": [
    "## 总结  \n",
    "贝叶斯因子较传统统计方法有很多优势，其中最突出的优势是对零假设和备择假设一视同仁。这一方面能够帮助研究者解决为零假设提供证据的问题，另一 方面还能帮助研究者拓宽思路，如本节课介绍了三种贝叶斯因子的计算与应用。  \n",
    "\n",
    "与传统的 $p$ 值不同，贝叶斯因子不仅能够告诉我们是否拒绝零假设，还能展示数据支持哪一个假设的证据强度。  \n",
    "\n",
    "最后，请大家不要谨慎看待 $p$ 值，$p$ 值并不教你相信/不相信什么，而只是为你修正自己的信念提供参考。  \n"
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